Answer:
c. Look at the first 7 digits in the table. Let digits from 0 to 3 ...
Step-by-step explanation:
The digits in a random number table are intended to be uniformly distributed, so that each digit has a probability of 0.1. By using combinations of digits you can fairly easily define an outcome that has a probability that is a multiple of 0.1.
Here, you want a probability of 40% = 0.4 = 4×0.1. By defining your outcome as any of 4 digit values, (0 to 3, for example), that outcome will have a probability of 0.4 = 40% when a digit is randomly chosen.
To choose the correct answer here, you only need to understand the above, then choose the answer choice that has an outcome that is defined as 4 of the digits.
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By looking at 7 digits, you effectively run a simulation in which you do the trial 7 times. Here, you're buying 7 boxes of cereal, so you're interested in 7 trials, each with a probability of success of 40%. This further confirms that the answer choice should include the wording "look at the first 7 digits."
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More explanation
If the first digit is a number 0-3, it means you got a toy in the first box of cereal.
If the second digit is a number 0-3, it means you got a toy in the second box of cereal.
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If the 7th digit is a number 0-3, it means you got a toy in the 7th box of cereal.
By counting the number of digits of the first 7 digits that are in the range 0-3, you are effectively counting the number of toys you got in those 7 boxes of cereal.
For example, if the first 7 digits of the table are 9656369*, there is only 1 digit in the range 0-3. That means this purchase of 7 boxes of cereal resulted in 1 toy.
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In order to answer Lydia's question, many groups of 7 digits would need to be evaluated, and the ratio of 2-toy purchases to total purchases computed from those results. A trial involving 7000 digits resulted in 268 purchases out of 1000 that had exactly 2 toys, for an experimental probability of 26.8%. Using the binomial distribution, the theoretical probability is about 26.1%--a fairly good match.
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* this number was generated by random [dot] org
